A) 50
B) -50
C) 40
D) -40
Correct Answer: B
Solution :
\[\because\] \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz=(x+y+z)\] \[({{x}^{2}}+{{y}^{2}}+{{z}^{2}}-xy-yz-zx)\] -Formula We do not know the value of \[xy+yz+zx\] . First find it. \[\because\] \[{{(x+y+z)}^{2}}={{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2\] \[(xy+yz+zx)-\] Formula \[({{10}^{2}}=30+2(xy+yz+zx)\] \[\Rightarrow\] \[2(xy+yz+zx)=100-30=70\] \[\therefore\] \[xy+yz+zx=\frac{70}{2}=35\] \[\therefore\] \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz\] \[=(x+y+z)({{x}^{2}}+{{y}^{2}}+{{z}^{2}}-xy-yz-zx)\] \[=10(30-35)\] \[=10\times -5=-50\]You need to login to perform this action.
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